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Articles 1  30 of 945
FullText Articles in Discrete Mathematics and Combinatorics
Laplacian Spectral Characterization Of Signed Sun Graphs, Fatemeh Motialah, Mohammad Hassan Shirdareh Haghighi
Laplacian Spectral Characterization Of Signed Sun Graphs, Fatemeh Motialah, Mohammad Hassan Shirdareh Haghighi
Theory and Applications of Graphs
A sun $SG_{n}$ is a graph of order $2n$ consisting of a cycle $C_{n}$, $n\geq 3$, to each vertex of it a pendant edge is attached. In this paper, we prove that unbalanced signed sun graphs are determined by their Laplacian spectra. Also we show that a balanced signed sun graph is determined by its Laplacian spectrum if and only if $n$ is odd.
Making Kr+1Free Graphs RPartite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender
Making Kr+1Free Graphs RPartite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender
Bernard Lidický
The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a Kr+1free graph on n vertices with e(G) > ex(n, Kr+1) − αn2, then one can remove εn2 edges from G to obtain an rpartite graph. Fu¨redi gave a short proof that one can choose α = ε. We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.
Sdrap: An Annotation Pipeline For Highly Scrambled Genomes, Jasper Braun
Sdrap: An Annotation Pipeline For Highly Scrambled Genomes, Jasper Braun
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Mathematical Models For Describing Molecular SelfAssembly, Margherita Maria Ferrari
Mathematical Models For Describing Molecular SelfAssembly, Margherita Maria Ferrari
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Loop Homology Of BiSecondary Structures, Andrei Bura
Loop Homology Of BiSecondary Structures, Andrei Bura
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova
Design Of Experiments For Unique Wiring Diagram Identification, Elena Dimitrova
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
On An Enhancement Of Rna Probing Data Using Information Theory, Thomas J.X. Li, Christian M. Reidys
On An Enhancement Of Rna Probing Data Using Information Theory, Thomas J.X. Li, Christian M. Reidys
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers, Erwin Cornelius
Research For Educators: Modeling Graph Theory For Nontraditional Math Researchers, Erwin Cornelius
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Making Kr+1Free Graphs RPartite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender
Making Kr+1Free Graphs RPartite, József Balogh, Felix Christian Clemen, Mikhail Lavrov, Bernard Lidický, Florian Pfender
Mathematics Publications
The Erdős–Simonovits stability theorem states that for all ε > 0 there exists α > 0 such that if G is a Kr+1free graph on n vertices with e(G) > ex(n, Kr+1) − αn2, then one can remove εn2 edges from G to obtain an rpartite graph. Fu¨redi gave a short proof that one can choose α = ε. We give a bound for the relationship of α and ε which is asymptotically sharp as ε → 0.
Sharp Bounds For Decomposing Graphs Into Edges And Triangles, Adam Blumenthal, Bernard Lidicky, Oleg Pikhurko, Yanitsa Pehova, Florian Pfender, Jan Volec
Sharp Bounds For Decomposing Graphs Into Edges And Triangles, Adam Blumenthal, Bernard Lidicky, Oleg Pikhurko, Yanitsa Pehova, Florian Pfender, Jan Volec
Bernard Lidický
Let pi3(G) be the minimum of twice the number of edges plus three times the number of triangles over all edgedecompositions of G into copies of K2 and K3. We are interested in the value of pi3(n), the maximum of pi3(G) over graphs G with n vertices. This specific extremal function was first studied by Gyori and Tuza [Decompositions of graphs into complete subgraphs of given order, Studia Sci. Math. Hungar. 22 (1987), 315320], who showed that pi3(n)<9n2/16.
In a recent advance on this problem, Kral, Lidicky, Martins and Pehova [arXiv:1710:08486] proved via flag ...
Fractional Strong Matching Preclusion For Two Variants Of Hypercubes, Huifen Ge, Tianlong Ma, Miaolin Wu, Yuzhi Xiao
Fractional Strong Matching Preclusion For Two Variants Of Hypercubes, Huifen Ge, Tianlong Ma, Miaolin Wu, Yuzhi Xiao
Theory and Applications of Graphs
Let F be a subset of edges and vertices of a graph G. If GF has no fractional perfect matching, then F is a fractional strong matching preclusion set of G. The fractional strong matching preclusion number is the cardinality of a minimum fractional strong matching preclusion set. In this paper, we mainly study the fractional strong matching preclusion problem for two variants of hypercubes, the multiply twisted cube and the locally twisted cube, which are two of the most popular interconnection networks. In addition, we classify all the optimal fractional strong matching preclusion set of each.
On The Second Least Distance Eigenvalue Of A Graph, Xueyi Huang, Qiongxiang Huang, Lu Lu
On The Second Least Distance Eigenvalue Of A Graph, Xueyi Huang, Qiongxiang Huang, Lu Lu
Lu Lu
Let $G$ be a connected graph on $n$ vertices, and let $D(G)$ be the distance matrix of $G$. Let $\partial_1(G)\ge\partial_2(G)\ge\cdots\ge\partial_n(G)$ denote the eigenvalues of $D(G)$. In this paper, the connected graphs with @n1(G) at least the smallest root of $x^3=3x^211x6 = 0$ are determined. Additionally, some nonisomorphic distance cospectral graphs are given.
Colored Complete Hypergraphs Containing No Rainbow Berge Triangles, Colton Magnant
Colored Complete Hypergraphs Containing No Rainbow Berge Triangles, Colton Magnant
Theory and Applications of Graphs
The study of graph Ramsey numbers within restricted colorings, in particular forbidding a rainbow triangle, has recently been blossoming under the name GallaiRamsey numbers. In this work, we extend the main structural tool from rainbow triangle free colorings of complete graphs to rainbow Berge triangle free colorings of hypergraphs. In doing so, some other concepts and results are also translated from graphs to hypergraphs.
Spn Graphs, Leslie Hogben, Naomi ShakedMonderer
Spn Graphs, Leslie Hogben, Naomi ShakedMonderer
Electronic Journal of Linear Algebra
A simple graph G is an SPN graph if every copositive matrix having graph G is the sum of a positive semidefinite and nonnegative matrix. SPN graphs were introduced in [N. ShakedMonderer. SPN graphs: When copositive = SPN. Linear Algebra Appl., 509:82{113, 2016.], where it was conjectured that the complete subdivision graph of K4 is an SPN graph. This conjecture is disproved, which in conjunction with results in the ShakedMonderer paper show that a subdivision of K_4 is a SPN graph if and only if at most one edge is subdivided. It is conjectured that a graph is an ...
Alpha Adjacency: A Generalization Of Adjacency Matrices, Matt Hudelson, Judi Mcdonald, Enzo Wendler
Alpha Adjacency: A Generalization Of Adjacency Matrices, Matt Hudelson, Judi Mcdonald, Enzo Wendler
Electronic Journal of Linear Algebra
B. Shader and W. So introduced the idea of the skew adjacency matrix. Their idea was to give an orientation to a simple undirected graph G from which a skew adjacency matrix S(G) is created. The adjacency matrix extends this idea to an arbitrary field F. To study the underlying undirected graph, the average characteristic polynomial can be created by averaging the characteristic polynomials over all the possible orientations. In particular, a HararySachs theorem for the averagecharacteristic polynomial is derived and used to determine a few features of the graph from the averagecharacteristic polynomial.
On Sign Pattern Matrices That Allow Or Require Algebraic Positivity, Diane Christine Pelejo, Jean Leonardo Abagat
On Sign Pattern Matrices That Allow Or Require Algebraic Positivity, Diane Christine Pelejo, Jean Leonardo Abagat
Electronic Journal of Linear Algebra
A square matrix M with real entries is algebraically positive (AP) if there exists a real polynomial p such that all entries of the matrix p(M) are positive. A square sign pattern matrix S allows algebraic positivity if there is an algebraically positive matrix M whose sign pattern is S. On the other hand, S requires algebraic positivity if matrix M, having sign pattern S, is algebraically positive. Motivated by open problems raised in a work of Kirkland, Qiao, and Zhan (2016) on AP matrices, all nonequivalent irreducible 3 by 3 sign pattern matrices are listed and classify into ...
On Orthogonal Matrices With Zero Diagonal, Robert F. Bailey, Robert Craigen
On Orthogonal Matrices With Zero Diagonal, Robert F. Bailey, Robert Craigen
Electronic Journal of Linear Algebra
This paper considers real orthogonal $n\times n$ matrices whose diagonal entries are zero and offdiagonal entries nonzero, which are referred to as $\OMZD(n)$. It is shown that there exists an $\OMZD(n)$ if and only if $n\neq 1,\ 3$, and that a symmetric $\OMZD(n)$ exists if and only if $n$ is even and $n\neq 4$. Also, a construction of $\OMZD(n)$ obtained from doubly regular tournaments is given. Finally, the results are applied to determine the minimum number of distinct eigenvalues of matrices associated with some families of graphs, and the related notion of orthogonal ...
On The Block Structure And Frobenius Normal Form Of Powers Of Matrices, Mashael M. Al Baidani, Judi J. Mcdonald
On The Block Structure And Frobenius Normal Form Of Powers Of Matrices, Mashael M. Al Baidani, Judi J. Mcdonald
Electronic Journal of Linear Algebra
The Frobenius normal form of a matrix is an important tool in analyzing its properties. When a matrix is powered up, the Frobenius normal form of the original matrix and that of its powers need not be the same. In this article, conditions on a matrix $A$ and the power $q$ are provided so that for any invertible matrix $S$, if $S^{1}A^qS$ is block upper triangular, then so is $S^{1}AS$ when partitioned conformably. The result is established for general matrices over any field. It is also observed that the contributions of the index of cyclicity ...
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker
Jeffrey S. Ovall
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of ...
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker
Jay Gopalakrishnan
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of ...
Classification Of Minimal Separating Sets In Low Genus Surfaces, J. J. P. Veerman, William Maxwell, Victor Rielly, Austin K. Williams
Classification Of Minimal Separating Sets In Low Genus Surfaces, J. J. P. Veerman, William Maxwell, Victor Rielly, Austin K. Williams
J. J. P. Veerman
Consider a surface S and let M ⊂ S. If S \ M is not connected, then we say M separates S, and we refer to M as a separating set of S. If M separates S, and no proper subset of M separates S, then we say M is a minimal separating set of S. In this paper we use computational methods of combinatorial topology to classify the minimal separating sets of the orientable surfaces of genus g = 2 and g = 3. The classification for genus 0 and 1 was done in earlier work, using methods of algebraic topology.
Of Matroid Polytopes, Chow Rings And Character Polynomials, Ahmed Ashraf
Of Matroid Polytopes, Chow Rings And Character Polynomials, Ahmed Ashraf
Electronic Thesis and Dissertation Repository
Matroids are combinatorial structures that capture various notions of independence. Recently there has been great interest in studying various matroid invariants. In this thesis, we study two such invariants: Volume of matroid base polytopes and the Tutte polynomial. We gave an approach to computing volume of matroid base polytopes using cyclic flats and apply it to the case of sparse paving matroids. For the Tutte polynomial, we recover (some of) its coefficients as degrees of certain forms in the Chow ring of underlying matroid. Lastly, we study the stability of characters of the symmetric group via character polynomials. We show ...
Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr
Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr
Journal of Humanistic Mathematics
"BEWARE and WARNING! This book is different from other books. You and YOU ALONE are in charge of what happens in this story." This is the captivating introduction to every book in the interactive novel series, Choose Your Own Adventure (CYOA). Our project uses the mathematical field of graph theory to analyze forty books from the CYOA book series for ages 912. We first began by drawing the digraphs of each book. Then we analyzed these digraphs by collecting structural data such as longest path length (i.e. longest story length) and number of vertices with outdegree zero (i.e ...
Coloring Count Cones Of Planar Graphs, Zdenek Dvorak, Bernard Lidicky
Coloring Count Cones Of Planar Graphs, Zdenek Dvorak, Bernard Lidicky
Bernard Lidický
For a plane neartriangulation G with the outer face bounded by a cycle C, let n⋆G denote the function that to each 4coloring ψ of C assigns the number of ways ψ extends to a 4coloring of G. The blockcount reducibility argument (which has been developed in connection with attempted proofs of the Four Color Theorem) is equivalent to the statement that the function n⋆G belongs to a certain cone in the space of all functions from 4colorings of C to real numbers. We investigate the properties of this cone for C=5, formulate a conjecture strengthening the ...
Coloring Count Cones Of Planar Graphs, Zdenek Dvorak, Bernard Lidicky
Coloring Count Cones Of Planar Graphs, Zdenek Dvorak, Bernard Lidicky
Mathematics Publications
For a plane neartriangulation G with the outer face bounded by a cycle C, let n⋆G denote the function that to each 4coloring ψ of C assigns the number of ways ψ extends to a 4coloring of G. The blockcount reducibility argument (which has been developed in connection with attempted proofs of the Four Color Theorem) is equivalent to the statement that the function n⋆G belongs to a certain cone in the space of all functions from 4colorings of C to real numbers. We investigate the properties of this cone for C=5, formulate a conjecture strengthening the ...
NonSparse Companion Matrices, Louis Deaett, Jonathan Fischer, Colin Garnett, Kevin N. Vander Meulen
NonSparse Companion Matrices, Louis Deaett, Jonathan Fischer, Colin Garnett, Kevin N. Vander Meulen
Electronic Journal of Linear Algebra
Given a polynomial $p(z)$, a companion matrix can be thought of as a simple template for placing the coefficients of $p(z)$ in a matrix such that the characteristic polynomial is $p(z)$. The Frobenius companion and the more recentlydiscovered Fiedler companion matrices are examples. Both the Frobenius and Fiedler companion matrices have the maximum possible number of zero entries, and in that sense are sparse. In this paper, companion matrices are explored that are not sparse. Some constructions of nonsparse companion matrices are provided, and properties that all companion matrices must exhibit are given. For example, it is ...
Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix
Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix
Masters Theses & Specialist Projects
This thesis explores functionally Alexandroff topologies and the order theory asso ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set.
The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies ...
ListDistinguishing Cartesian Products Of Cliques, Michael Ferrara, Zoltan Füredi, Sogol Jahanbekam, Paul Wenger
ListDistinguishing Cartesian Products Of Cliques, Michael Ferrara, Zoltan Füredi, Sogol Jahanbekam, Paul Wenger
Sogol Jahanbekam
The Mystery Of Frobenius Symmetry, Maciej Piwowarczyk
The Mystery Of Frobenius Symmetry, Maciej Piwowarczyk
DePaul Discoveries
In this project we studied the mathematical concept of the Frobenius number and some curious patterns that come with it. One common example of the Frobenius number is the Coin Problem: If handed two denominations of coins, say 4¢ and 5¢, and asked to create all possible values, we will eventually find ourselves in a position where we can make any value. With 4¢ and 5¢ coins, we can create any value above 11¢, but not 11¢ itself. So, that makes 11 the Frobenius number of 4 and 5. What we explore in this paper is a pattern we call ...
Analogues Between Leibniz's Harmonic Triangle And Pascal's Arithmetic Triangle, Lacey Taylor James
Analogues Between Leibniz's Harmonic Triangle And Pascal's Arithmetic Triangle, Lacey Taylor James
Electronic Theses, Projects, and Dissertations
This paper will discuss the analogues between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle by utilizing mathematical proving techniques like partial sums, committees, telescoping, mathematical induction and applying George Polya's perspective. The topics presented in this paper will show that Pascal's triangle and Leibniz's triangle both have hockey stick type patterns, patterns of sums within shapes, and have the natural numbers, triangular numbers, tetrahedral numbers, and pentatope numbers hidden within. In addition, this paper will show how Pascal's Arithmetic Triangle can be used to construct Leibniz's Harmonic Triangle and show how both triangles ...